According to known processes, metallurgical slags such as obtained from the smelting of non-ferrous metal concentrates that contain metal values such as zinc, tin, lead, cadmium, indium, arsenic, antimony and germanium are subjected to a continuous or batch-wise fuming operation by supplying slag in molten or solid form, an oxygen-containing gas, and a fuel and reductant such as natural gas or fuel gas, coal or coke to a fuming furnace. The vapors emanating from the furnace contain the volatile constituents from the slag which are condensed and the condensed metal values are recovered. Alternatively, the vapors are oxidized, condensed and recovered as oxide fumes. In the latter case, the amount of oxygen in the oxygen-containing gas should be sufficient to maintain the temperatures in the furnace sufficiently high, e.g., 1100.degree.-1300.degree. C., to enable the removal of the volatile constituents from the slag. Additional oxygen-containing gas may be supplied above the slag to ensure complete combustion of the reductant and oxidation of metal values to oxides.